Download Cats protecting birds] modelling the mesopredator release effect

Journal of Animal
Ecology 0888\
57\ 171Ð181
Cats protecting birds] modelling the mesopredator
release effect
FRANCK COURCHAMP\ MICHEL LANGLAIS$ and
GEORGE SUGIHARA
Scripps Institution of Oceanography\ University of California San Diego\ 8499 Gilman Drive Ð La Jolla\ CA
81982Ð9191\ USA^ and $ERS CNRS 012 {Mathematiques Appliquees de Bordeaux|\ Universite Victor Segalen
Bordeaux 1\ 035 rue Leo Saignat\ F!22965 Bordeaux Cedex\ France
Summary
0[ Introduced predators account for a large part of the extinction of endemic insular
species\ which constitutes a major component of the loss of biodiversity among
vertebrates[ Eradication of alien predators from these ecosystems is often considered
the best solution[
1[ In some ecosystems\ however\ it can generate a greater threat for endemic prey
through what is called the {mesopredator release|[ This process predicts that\ once
superpredators are suppressed\ a burst of mesopredators may follow which leads their
shared prey to extinction[
2[ This process is studied through a mathematical model describing a three species
system "preyÐmesopredatorÐsuperpredator#[ Analysis of the model\ with and without
control of meso! and superpredators\ shows that this process does indeed exist and
can drive shared prey to rapid extinction[
3[ This work emphasizes that\ although counter!intuitive\ eradication of introduced
superpredators\ such as feral domestic cats\ is not always the best solution to protect
endemic prey when introduced mesopredators\ such as rats\ are also present[
Key!words] bird conservation\ feral cats\ introduced mammals\ control strategy\ rats[
Journal of Animal Ecology "0888# 57\ 171Ð181
Introduction
Most contemporary worldwide extinctions have
occurred\ or are currently occurring in island eco!
systems[ As an example\ of the 29 species of reptiles
and amphibians that have gone extinct since 0599\
more than 89) are island forms "Honnegger 0870#^
82) of 065 species or subspecies of birds "King 0874#\
and 70) of 54 mammal species extinctions "Ceballos
+ Brown 0884# that have occurred during this period
have occurred on islands[
The introduction of vertebrate species is one of the
most important threats to many endemic species in
many islands "Moors + Atkinson 0873^ Atkinson
0878#[ Numerous rare or endemic vertebrate species
are currently endangered because of predation by
introduced invertebrates\ reptiles\ birds or mammals\
Þ 0888 British
Ecological Society
171
Correspondence] Franck Courchamp\ Department of
Zoology\ University of Cambridge\ Downing Street\ Cam!
bridge\ CB1 2EJ\ UK[ E!mail fc108Ýcam[ac[uk[ Tel] 90112!
225532[ Fax] 90112!225565[
or by competition from or habitat destruction by
introduced grazers such as rabbits "Oryctolagus cun!
iculus\ Lilljeborg# or goats "Capra hircus\ L[# "Moors
+ Atkinson 0873^ Atkinson 0878^ Williamson 0885#[
According to King "0874#\ predation by introduced
animals has been a major cause of 31) of island
bird extinctions in the past\ and is a major factor
endangering 39) of currently threatened island bird
species[ In particular\ introduced feral cats "Felis
catus\ L[# are known to be a major threat to many
island bird species[ They are known to have been
introduced into at least 54 island groups where they
are responsible for the loss of many large land and
seabird colonies\ populations or even species "e[g[ Jou!
ventin et al[ 0873^ Rodriguez!Estrella et al[ 0880^ Mon!
teiro\ Ramos + Furness 0885#^ for example\ a few
cats "around _ve# were introduced to the Kerguelen
Islands in the mid!century[ They are now responsible
for the decline or extinction of several bird popu!
lations in these islands\ killing more than 2 million
petrels per year "Chapuis 0884#[ Cats also constitute
a major threat to many endemic reptile species or
172
F[ Courchamp\
M[ Langlais +
G[ Sugihara
Þ 0888 British
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Journal of Animal
Ecology\ 57\ 171Ð181
subspecies "e[g[ Iverson 0867^ Case + Bolger 0880^
Arnaud et al[ 0882# and mammals "Spencer 0880^ Mel!
link 0881#[ Their impact has also been demonstrated
through competition towards endemic mammalian
predators such as island foxes "e[g[ Urocyon littoralis
dickeyi\ Baird#\ which they replace when uncontrolled
"Steve Kovach\ personal communication#[
Eradication of those alien cat populations is
required in many cases\ has often been tried\ some!
times achieved "Rauzon 0874^ Veitch 0874^ Domm
+ Messersmith 0889^ Cooper 0884# and several cat
eradication programmes are currently underway[
Paradoxically\ in some particular situations\ the pres!
ence of a controlled population of cats might be\ at
least temporarily\ more bene_cial to their endemic
prey than its eradication[ Such is the case on many
islands where rodents have also been introduced[
Indeed\ it has been shown that the di}erent species
of introduced rats "Kiore or Polynesian or Paci_c rat
Rattus exulans\ F[\ Black or Roof or Ship rat\
R[ rattus\ F[ and Brown or Norwegian rat R[ nor!
vegicus\ F[# have an extremely deleterious e}ect on
numerous species of amphibians "e[g[ Thurley + Ben
0883^ Towns + Daugherty 0883#\ reptiles "e[g[ Mac!
Callum 0875^ Newman + McFadden 0889^ Case\
Bolger + Richman 0881^ Cree\ Daugherty + Hay
0884#\ birds "e[g[ Atkinson 0874^ Konecny 0876^
Bertram + Nagorsen 0884# and even mammals "e[g[
Brosset 0852^ Bell 0867^ Atkinson 0874#[ This e}ect
can be indirect\ such as through competition for shel!
ter\ nest!sites "Seto + Conant 0885# or food\ as the
diet of rats comprises mainly berries\ leaves\ seeds and
invertebrates "Clark 0879\ 0870#[ Rats can also have
a direct e}ect\ through predation[ Indeed\ these three
introduced species of rat are known to prey on eggs\
chicks\ juveniles and even adults of ground!nesting
seabirds and land birds "e[g[ Kepler 0856^ Bertram
0884^ Brooke 0884^ Lovegrove 0885# and even tree!
nesting birds "e[g[ Campbell 0880^ Seitre + Seitre 0881^
Amarasekare 0882#[ In total\ R[ exulans predation is
documented on at least 04 di}erent bird species\
R[ rattus predation on at least 28 bird species\ and
R[ norvegicus on at least 42 bird species "for a review\
see Atkinson 0874#[ Not only do rats have a potential
impact on numerous species throughout the world
"they are known to have colonized at least 71) of the
012 major island groups\ Atkinson 0874#\ but they
sometimes cause extremely rapid extinctions on newly
colonized islands[ A well!known example is the estab!
lishment around 0853 of black rats on Big South Cape
Island\ New Zealand\ causing the local loss of three
New Zealand endemic birds\ and the complete extinc!
tion of two more\ and of one species of bat\ in less
than 1 years "Bell 0867#[ Introduced house mice "Mus
musculus\ L[# also have a potential negative impact on
vertebrate species\ by competition or direct predation
"e[g[ Moors + Atkinson 0873^ Johnstone 0874^ New!
man 0883#[
The domestic cat is an opportunist predator "Fitz!
gerald 0877#[ When both bird and mammal prey are
available\ it is believed that the domestic cat diet will
include mainly mammals "e[g[ Konecny 0876^ Nogales
et al[ 0881^ Nogales + Medina 0885#[ In some island
ecosystems\ these cats maintain rodent populations
at low levels[ Although they also often prey upon
endangered species\ it is believed that\ in some eco!
systems at least\ the bene_cial e}ects of reducing the
rodent population could outweigh the damage done
to the endemic prey species "Fitzgerald et al[ 0880^
Tidemann\ Yorkston + Russack 0883#[ The threat
posed by introduced cats to the kakapo "Strigops hab!
roptilus\ Gray# on Stewart Island is a striking example[
Here\ cats prey lightly on this highly endangered bird
species "remains were found in 4=0) of 007 collected
scats\ Karl + Best 0871#\ but even low predation pres!
sure may be detrimental for fragile species "Rod!
riguez!Estrella et al[ 0880#[ However\ rat remains were
found in 82=9) of these 007 scats "Karl + Best 0871#\
showing the indirect role cats might play in preserving
native fauna through reduction of rat predation pres!
sure on the kakapo[ Moreover\ the elimination of feral
cat populations from such ecosystems could lead to a
more severe negative impact on the endemic species\
as a result of expansion of rodent populations once
their predators are removed[ Attempted reduction of
the cat population of Amsterdam Island is alleged to
have caused a compensating rise in the number of rats
and mice\ and so has been abandoned "Holdgate +
Wace 0850#[ This process\ termed {mesopredator
release|\ had been described in fragmented insular eco!
systems "Soule et al[ 0877# and applies well to many
insular foodwebs "e[g[ Schoener + Spiller 0876#[ Con!
versely\ the eradication of rodents _rst "which has
now proven feasible\ even on relatively large islands\
Taylor + Thomas 0878\ 0882^ Towns 0885# might
induce cats to switch prey\ resulting in a brutal
increase in predation pressure on the threatened
endemic species\ as experienced for stoats and rats in
New Zealand "Murphy + Brad_eld 0881#[ Unfor!
tunately "from the theoretical point of view#\ there is
little _eld evidence from island management either of
mesopredator release following superpredator eradi!
cation\ or of predators switching prey following meso!
predator eradication[
As the optimal control strategy is neither simple to
_nd nor intuitive\ it is studied through the analysis of
a mathematical model which mimics the dynamics of
the three species in this system[ In the study reported
here\ the interactions of a prey species\ such as a bird
species\ a threatening alien mesopredator\ such as a
rat\ and an alien superpredator species\ such as the
feral domestic cat\ were examined through their
coupled dynamics[ Through this model\ the theor!
etical existence of {mesopredator release| and the e}ect
of the presence of a superpredator on the prey will be
investigated[ It is assumed that the superpredator
preys both upon the prey and the mesopredator[ For
the sake of simplicity\ reference will sometimes be
173
Mesopredator
release in insular
ecosystems
made to them as bird\ rat and cat\ instead of prey\
mesopredator and superpredator\ respectively[
The prey:mesopredator "bird:rat# system is given
by]
The models
FdB
B
B
G dt rbB 0 − K − S ¦ B hbR
b
j
JdR
hbhsR
G rrR 0 −
hbS ¦ hsB
f dt
THE PRELIMINARY MODELS
Þ 0888 British
Ecological Society
Journal of Animal
Ecology\ 57\ 171Ð181
For the sake of simplicity\ models are _rst presented
taking into account only two species\ and only then is
the third species added and its implied complications
analysed[ The construction and analysis of the models
are based on previous work "Courchamp + Sugihara
0888#\ to which the reader can refer for additional
details[ The _rst two systems consist of two simple
coupled di}erential equations\ each representing the
dynamics of one population[ Each population is
described by a simple logistic equation\ modi_ed to
take into account its relationship with the other spec!
ies[ The other possible prey species populations are
not taken into account^ it is assumed that all the prey
species form a single {bird| population\ with average
characteristics[ The realism of these assumptions has
been discussed previously "Courchamp + Sugihara
0888#[ The number of individuals at time t in the prey\
mesopredator and superpredator populations are B\
R and C\ respectively[ The intrinsic growth rates of
the prey\ mesopredator and superpredator popu!
lations are rb\ rr and rc\ respectively[ The predation
rate of the superpredator is mb on the prey and mr on
the mesopredator[ The predation rate of the meso!
predator is hb on the prey and hs on other food items
"seeds\ leaves\ invertebrates#[ The carrying capacity of
the environment for the prey population is Kb[ The
carrying capacities of the environment for the meso!
predator and the superpredator populations are not
constants\ but depend partially "rats are omnivores# or
totally "cats are carnivores# on the number of available
individual prey on which their populations can feed
at time t[ For the mesopredator\ the carrying capacity
of the environment is the number of mesopredators
that can live on food other than birds when there is
no prey\ to which is added the number of meso!
predators that can be fed by the total of available prey
at time t[ The carrying capacity is thus the quantity of
non!avian food S divided by the consumption rate hs\
plus the number of prey B divided by the meso!
predator predation rate hb] S:hs ¦ B:hb\ that is
"hbS ¦ hsB#:hbhs[ For the sake of simplicity\ it is
assumed that S is a constant "the carrying capacity in
the absence of prey is kept under the form S:hs instead
of a constant\ say Ks\ to conserve homogeneous
notation#[ Rats are opportunistic predators\ and their
diet "proportion of avian and non!avian food con!
sumed# depends on relative availability of food items
"Clark 0879#[ Accordingly\ instead of hbR\ the pre!
dation rate of rats on birds is] BhbR:"S¦B#[ In the
two!species models\ the rat:cat system is not
presented\ because it is the same as the bird:cat system[
0
0
1
1
eqn 0
eqn 1
There are several equilibrium points[ The _rst two
equilibrium states\ extinction of both populations ð9\
9Ł and extinction of the rat only ðKb\ 9Ł are always
unstable[ The third state\ extinction of the bird only\
"9\ S:hs# is globally asymptotically stable if and only
if rb ¾ hb:hs[ These three points always exist[ When
both populations coexist\ the system reaches "B\
S:hs ¦ B:hb#[ B is given in the Appendix with the
analysis of the system[
The prey:superpredator "bird:cat# system is given
by]
0
0
1
1
FdB
B
G dt rbB 0 − K − mbC
b
j
JdC
mC
G rcC 0 − b
B
f dt
eqn 2
eqn 3
It is the same for the mesopredator:superpredator
"rat:cat# system "B is replaced by R and b indices are
replaced by r indices#[ They have three stable equi!
librium points only\ as the predator cannot survive
alone] ð9\ 9Ł\ ðKb\ 9Ł and ðKb"0 − 0:rb#\
Kb"0 − 0:rb#:mbŁ[
THE COMPLETE MODEL
To take the three species into account simultaneously\
one needs to make further assumptions[ First of all\
like the rat\ the domestic cat is an opportunist pred!
ator\ which switches prey species according to their
availability "Fitzgerald 0877#[ Accordingly\ the num!
ber of birds and rats preyed upon by cats will depend
on their respective numbers[ Instead of mbC and mrC\
one will _nd] mbBC:"B¦R# and mrRC:"B¦R# for the
bird and the rat populations\ respectively[ Potential
preferences of the cat for the indigenous prey over the
introduced predator are not taken into account "see
Courchamp\ Langlais + Sugihara\ in press#[ The cat
carrying capacity is] B:mb ¦ R:mr[ The compartmental
representation of the model is given in Fig[ 0[
One has the following system]
FdB
B
B
B
G rbB 0 −
−
hbR −
mC
dt
K
S
¦
B
B
¦
R b
b
G
G
eqn 4
G
GdR
hbhsR
R
G rrR 0 −
−
mrC
hbS ¦ hsB
B¦R
g dt
G
eqn 5
G
G
GdC rcC 0 − mbmrC
mrB ¦ mbR
G dt
G
eqn 6
f
0
1
0
1
0
1
174
F[ Courchamp\
M[ Langlais +
G[ Sugihara
Fig[ 0[ Compartmental representation of the mathematical model with three species "eqns 6\ 7\ 8#[ Each box represents one
population\ symbolized by a letter and an animal] superpredator "C\ cats#\ mesopredator "R\ rats# and prey "B\ birds#[ The
arrows represent the ~ux within and are between compartments] curved arrows are intrinsic growth rates^ straight arrows are
predation rates[ The intrinsic growth rates of the superpredator\ the mesopredator and the prey are rc\ rr and rb\ respectively[
The predation rates of the superpredator on the mesopredator and on the prey are mr and mb\ respectively^ the predation rate
of the mesopredator on the prey is hb[
There are several states with this system] all popu!
lations go extinct ð9\ 9\ 9Ł\ only the prey survives ðKb\
9\ 9Ł\ only the mesopredator survives ð9\ S:hs\ 9Ł\ only
the superpredator disappears ðB\ S:hs ¦ B:hb\ 9Ł "B
has the same value than in system "0Ð1##\ only the prey
disappears ð9\ S:hs"0 − 0:rr#\ S:mrhs"0 − 0:rr#Ł\ only the
mesopredator disappears ðKb "0 − 0:rb#\ 9\
Kb"0−0rb#:mbŁ\ and\ _nally\ no species disappears ðB5\
R5\ C5Ł[ There can be between 9 and 4 stationary
states with the equilibrium value of B between 9 and
Kb\ as solutions of an equation of the _fth degree[ As
its expression is very long and complex for the last
point\ it will not be presented here\ but the authors
will provide the Maple _le upon request[ For the same
reason\ the comparison between di}erent points is
too complex to be presented here analytically[ The
deterministic nature of the model allows\ however\ a
numerical study[
It can be noted that the fourth\ _fth and sixth equi!
librium points are equivalent to some from the models
0Ð1 and 2Ð3[ The conditions of existence of these
points are described in the Appendix[
SUPERPREDATOR PRESENCE AND
MESOPREDATOR RELEASE
Þ 0888 British
Ecological Society
Journal of Animal
Ecology\ 57\ 171Ð181
The behaviour of the model is studied analytically "see
Appendix#\ but simulations are presented for heuristic
purposes[ It can be seen from Fig[ 1 that\ under some
conditions\ while the rat alone would extirpate the
bird "a# and the cat alone would not "b#\ the cat pre!
vents extinction of the bird by the rat when both
predators are present by controlling rat "c#\ or even
by extirpating the rat "d#[
One can see that\ in some cases\ the presence of the
superpredator can indirectly protect a shared prey
from a mesopredator[ Even in circumstances where
this is not the case\ the elimination of the super!
predator might be more harmful to the prey\ through
the {mesopredator release|\ which arises when the pres!
sure on mesopredators by superpredators is
suppressed[ To mimic this process\ the e}ect of the
suppression of the superpredator when the three spec!
ies are present in equilibrium is studied[ First one has
to _nd values for which the bird population does not
go extinct when the two other species are introduced[
A range of parameters must be de_ned at which all
three populations persist and reach an equilibrium
state[ This range of parameters implies high values of
intrinsic growth rate of the prey "×0=2# if it is to
survive the presence of the two predators[ From this
equilibrium state "ðB5\ R5\ C5Ł#\ the extinction of
the superpredator population can be simulated and
the outcome of the two remaining populations moni!
tored] new simulations are run with the following
initial conditions] ðB5\ R5\ 9Ł[ This is repeated for
di}erent values of sensible parameters\ to obtain a
pattern displayed Fig[ 2[ This shows that prey extinc!
tion through mesopredator release does occur in this
system[ Moreover\ it is avoided only for higher values
of prey intrinsic growth rate "×0=5#[ These correspond
to values too high to be biologically realistic\ and will
not often be reached in natura by insular bird species[
Indeed\ in the absence of similar predation pressure\
175
Mesopredator
release in insular
ecosystems
Fig[ 1[ Simulations showing the dynamics of the three population sizes plotted against time] "a# the model with only prey and
mesopredator "system 0Ð1#^ "b# the model with only prey and superpredator "system 2Ð3#^ "c# and "d# the model with prey and
both mesopredator and superpredator "system 4Ð6#[ The values used for the simulations show that the superpredator can
lower the mesopredator population\ to such a point that it prevents the prey elimination ðsimple mesopredator control in "c#\
total mesopredator eradication in "d#Ł[ Values used are 0=4\ 3=9 and 9=64 for rb\ rr and rc\ respectively\ 099 999 for Kb and 09999
for S\ 43 for mb and 199 for mr\ 5 for hb and 254 for hs[ Initial conditions are in all cases 099 999 birds\ 099 rats and 0 cat "which
corresponds to the introduction of 099 rats and:or 0 cat into a healthy population of 099 999 birds#[ The scale is di}erent for
the three species[
Þ 0888 British
Ecological Society
Journal of Animal
Ecology\ 57\ 171Ð181
Fig[ 2[ Phase portrait of the bird vs[ the rat populations\ displaying the e}ect of the eradication of the superpredator on the
prey\ for di}erent values of the prey intrinsic growth rate[ Initial conditions are here the equilibrium point of the model where
all three species are present "cat population is set to zero to simulate its eradication#[ This point changes because di}erent
values are used for the prey intrinsic growth rate leading to di}erent equilibrium values[ Elimination of the superpredator
without elimination of the mesopredator results in elimination of the prey population through {mesopredator release|\ when
the prey intrinsic growth rate is lower than 0=5 "curves in light grey#[
176
F[ Courchamp\
M[ Langlais +
G[ Sugihara
these endemic species seldom have developed anti!
predator life history traits\ such as a high intrinsic
growth rate[ These results show that the only endemic
species with intrinsic growth rates high enough to
survive the introduction of both a superpredator and
a mesopredator will normally be extirpated through
mesopredator release if the control strategy implies
only the superpredator eradication[ The strategy of
control therefore appears essential in these particular
ecosystems[
CONTROL STRATEGY
Mesopredator release can occur following eradication
of the superpredator and the presence of the super!
predator also has negative e}ects on the prey popu!
lation\ therefore a study of control strategies is neces!
sary to determine an optimal strategy[ If one applies
a control e}ort of lr on the rat population and of lc
on the cat population\ the model "4Ð6# becomes]
FdB
B
B
B
G rbB 0 −
−
h bR −
mbC
dt
K
S
¦
B
B
¦
R
b
G
G
eqn 7
G
GdR
hbhsR
R
G rrR 0 −
−
m C − lrR
hbS ¦ hsB
B¦R r
g dt
G
eqn 8
G
G
GdC rcC 0 − mbmrC
− lcC
mrB ¦ mbR
G dt
G
eqn 09
f
0
1
0
1
0
1
This provides the same number of equibrium points
as model "4Ð6#\ although with di}erent values[ Values
of these points are provided in the Appendix\ together
with their conditions of existence and stability[
Analysis of this model shows that when super!
predator control is high enough "lc × rc#\ the super!
predator disappears[ As a result\ the prey also dis!
appears when the mesopredator control is not high
enough ðlr ³ rr"0 − rbhs:hb# ³ rr#\ because of meso!
predator release[ In contrast\ and surprisingly\ the
prey does not disappear when the superpredator con!
trol is below a certain threshold ði[e[ rc"0 − rb# ³
lc ³ rcŁ\ provided the mesopredator control is high
enough ðlr × rr − mr"0 − lc:rc#:mbŁ[ This illustrates the
importance of the presence of the superpredator in
the system\ and the need to take it into account in
control programmes[
Discussion
Þ 0888 British
Ecological Society
Journal of Animal
Ecology\ 57\ 171Ð181
This study examined\ through a mathematical model\
the fate of a prey species in an insular ecosystem into
which both a mesopredator and a superpredator have
been introduced[ Although other species could have
been considered\ such as mongooses and reptiles "Case
et al[ 0881#\ the rat\ feral cat and endemic bird species
were taken as examples[ Indeed\ as Diamond "0878#
stated\ {rats and cats are the most notorious killers
and island birds the most notorious victims\ in this
regard ðextinctions due to introduced predatorsŁ[| This
work shows several interesting features of direct con!
cern to conservation biology[ First\ the result of this
theoretical work shows that the presence of one pred!
ator only is su.cient to induce the extinction of the
endemic prey[ This is not new\ as indicated by too
many examples in natura[ Second\ when both the
mesopredator and the superpredator are present\
seven di}erent situations may arise\ among which is
the case where the three species are present with stable
dynamics[ Interestingly\ there is another case where
both predator species can coexist inde_nitely\ even
after the eradication of the prey species[ Finally\ and
most interestingly\ is the case where the superpredator
causes the extinction of the mesopredator\ but not of
the prey[
It has been shown here that presence of a super!
predator may have a global positive e}ect in insular
ecosystems in which an introduced mesopredator
threatens an endemic prey[ Indeed\ in the model pre!
sented here the presence of the superpredator may
preclude the elimination of the prey by the meso!
predator "or allow a larger prey population size#[ In
addition\ it has been demonstrated that superpredator
eradication should be avoided\ as a means to prevent
what has been termed {mesopredator release| "Soule
et al[ 0877#] a sudden burst of mesopredators\ once
the superpredator pressure is suppressed[ Rats have a
lower predation rate on birds than cats\ but they are
much more numerous and can have a higher impact
on the prey "Newman + McFadden 0889#[ Moreover\
as they are omnivores\ they can maintain a high popu!
lation and a high predation pressure\ even when the
prey population size is low\ which the cat cannot[ This
explains why rats alone eliminate the prey more easily
than cats alone in the model "Fig[ 1#\ and why the cat
presence is sometimes bene_cial to shared prey[ In
fact\ over the last 399 years\ rats and cats are said to
be responsible for 43) and 15) of island extinctions
caused by predators\ respectively "King 0874#[ The
study of the control strategies clearly shows that the
fate of the prey will depend on the superpredator
control level[ Although counterintuitive\ if the super!
predator control is too high\ the prey will disappear[
This may be a further argument in favour of the use
of biological control\ especially with pathogens with a
steady long!term impact "see Courchamp + Sugihara
0888#\ which are unlikely to be too brutal[
Despite its mathematical complexity\ this model
remains very simple in its representation of the bio!
logical reality[ In particular\ spatial and temporal
population heterogeneities\ which are important com!
ponents of insular ecosystems\ were not taken into
account[ Similarly\ the fact that di}erent prey species
are present in these ecosystems has not been taken
into account[ Instead\ only one species\ which is sup!
177
Mesopredator
release in insular
ecosystems
Þ 0888 British
Ecological Society
Journal of Animal
Ecology\ 57\ 171Ð181
posed to represent the {average| of all prey species\ was
considered[ As the rats and the cats are opportunistic
predators\ which switch prey species according to their
relative availability "Clark 0879^ Fitzgerald 0877#\ it
would be interesting to study the e}ect of the presence
of several prey species[ This model is robust enough
to be extended to other ecosystems that can be well
described by the preyÐmesopredatorÐsuperpredator
trophic web[ It therefore holds for systems where sev!
eral prey species are present "e[g[ landbirds\ seabirds
and lizards# provided that they are prey of both the
mesopredator and the superpredator[ Some changes
may occur in the solutions of the model according to
the characterics of the species "e[g[ if they have di}er!
ent antipredation response#\ but the general con!
clusions should remain the same[ Similarly\ the results
will be the same if another superpredator\ say a bird
of prey\ is present[ Di}erent e.ciencies in hunting
di}erent preys would here again add more complexity[
In contrast\ the model results will undoubtedly be
di}erent if another species is present which does not
fully _t into one of these three trophic levels\ because
it would describe a totally di}erent system[ It is the
case\ for example\ if a prey species "e[g[ the rabbit# is
present which is not preyed upon by both the super!
predator and the mesopredator] islands where cats\
rats and rabbits have been introduced should there!
fore be described by a di}erent model[ Despite these
possible improvements\ this theoretical work shows
that it is crucial to take into account the presence of
other alien species when designing control pro!
grammes for one introduced species "see also Cour!
champ et al[\ in press for another example#[ Emphasis
is placed on the following important distinction that
should be understood from this work] in some eco!
systems where rats are present\ introduced cats might
play a positive role "implying that their removal could
have negative aspects on local fauna#^ however\ their
introduction cannot be recommended\ whatever the
circumstances[
Several points allow optimism about this particular
area of conservation biology[ First\ the recovery
and:or preservation of the ecosystems involved is not
in con~ict with local economic or politic interests\
even if the governments of many concerned islands
can hardly a}ord costly programmes such as mammal
eradications[ Second\ eradication of introduced mam!
mals such as domestic cats "Bloomer + Bester 0881#\
rabbits "Flux 0882#\ rats "Taylor + Thomas 0882#\
possums "Cowan 0881#\ foxes "Bailey 0881#\ goats
"Parkes 0889# or others\ once thought impossible\ is
now known to be feasible^ for example\ 019 successful
{pest| eradications have already been conducted on
New Zealand islands "Veitch et al[ 0881#[ Third\ many
studies show that\ when the introduced species has
been successfully removed from the whole ecosystem\
the threatened species "plant or animal# generally
recovers\ sometimes rapidly\ from the e}ects of these
alien species "e[g[ Cruz + Cruz 0876^ Brothers + Cop!
son 0877^ Towns 0880\ 0883^ Newman 0883^ Cooper
et al[ 0884#[ Fourth\ in the cases where alien species
induced the complete extinction of the population\
local populations were often concerned^ species or
subspecies extinctions are less frequent "Moors +
Atkinson 0873#[ Moreover\ seabird populations are
not dependent on the land for food\ and breeding
can continue on isolated islets and stacks free from
predators "Atkinson 0874#[ In most cases of colony or
population extinctions as a result of alien predators\
there are\ in nearby islets\ populations able to re!
colonize the ecosystem once the predator eradication
is achieved "Moors + Atkinson 0873^ Case et al[ 0881^
Jouventin + Micol 0884#[ Last\ in some cases "as in
the well known case of the kakapo\ Clout + Craig
0884^ Powlesland et al[ 0884# it is suspected that only
a small number of individuals "cats as well as rats#
have learned to kill the prey or eat the eggs "Grant\
Pettit + Whittow 0870^ Moors + Atkinson 0873#[ In
these cases\ when heavy programmes\ such as com!
plete eradication or long!term control\ are not poss!
ible\ selective control to eliminate these particular
individuals may be su.cient in the short term\ and
should thus be implemented[
However\ the situation is critical in many cases\ and
the media and scienti_c coverage of the situation on
most islands does not seem to be proportionate to
the problems faced by these often unique ecosystems
"Crystal 0878#[ Despite numerous indications of cata!
strophic e}ects of introduced mammals on most oce!
anic islands\ politically organized policies to resolve\
or even prevent these e}ects remain comparatively
few[ Recent examples\ and other older ones\ show
that solutions do exist[ It is often the high _nancial
constraints on eradication programmes that preclude
them "Powlesland et al[ 0884#\ or that impose unde!
sired priorities in the order of their attainment "Bro!
thers + Copson 0877#[ In these cases\ a predictive
study on the feasibility of the eradication and its
potential e}ects on the ecosystem is needed\ especially
when there is more than one introduced species\ in
order to maximize the e.ciency of eradication pro!
grammes[ Theoretical studies\ such as mathematical
modelling could ful_l this task[ This study shows that
the intuitively evident need for feral cat eradication
may not be the best solution in some speci_c cases\
such as when introduced rodents are present[ This is
well illustrated by the case of Raoul Island\ where it
has been said that eradication of feral cats might bring
little bene_t to bird populations\ because Norway rats
are present on this island and constitute a major part
of the diet of the cats "Fitzgerald et al[ 0880#[ Empirical
examples remain\ however\ scarce regarding the e}ects
of eradication of predators "top predators or meso!
predators# on population dynamics of coexisting
species[
The idea that top predators may be important spec!
ies for conservation biology is not new[ It has been
suggested that they have a disproportionate importance
178
F[ Courchamp\
M[ Langlais +
G[ Sugihara
in food webs because their extinction can gen!
erate a cascade of unexpected secondary extinctions
"Paine 0855^ Pimm 0879#[ For example\ the extinction
of several prey species has been attributed to the
increase of generalist and:or medium!sized predatory
mammals because of the lack of top predators in
di}erent ecosystems "Terborgh + Winter 0879^ Dia!
mond + Case 0875^ Wilcove\ McLellan + Dobson
0875^ Diamond 0878^ Bohning!Gaese\ Taper +
Brown 0882^ Goodrich + Buskirk 0884#[ With the
example of lynx\ mongooses and rabbits\ it has been
shown\ both theoretically and empirically\ that top
predators actually bene_t their prey through intra!
guild predation on other smaller predators which
share the prey "Palomares et al[ 0884#[ What is new
here is rather the application of this idea to an already
perturbed ecosystem\ a rather counter!intuitive idea]
in some cases the removal of one of the causes of
perturbation may lead to increased damage[ This is
the case with the mesopredator release "Soule et al[
0877#[ In some systems\ only the direct negative e}ects
of the top predator on endemic threatened prey have
been examined\ while in some cases greater positive
e}ects may be present on the same species[ Obviously\
outcomes of changes of these already perturbed tro!
phic webs are not intuitive\ and intervention as dra!
matic as species eradication should always be pre!
ceded by careful empirical and theoretical studies of
the whole ecosystem[ Indeed\ in the present case\ era!
dicating the rats before the cats "at _rst a seemingly
sound strategy# might in fact lead to another case of
mesopredator release\ as shown by the recent example
of Bird Island in the Seychelles[ Here\ a recent eradi!
cation of the introduced black rat population led to an
explosion of the exotic crazy ant Anoplolepis longipes\
Jerdon\ which has been shown to be threatening the
bird colonies which rat eradication was intended to
protect "Feare 0887#[ As complete removal of those
alien predators is most of the time "and often rightly#
the only envisaged solution "Veitch 0874^ Ashmole\
Ashmole + Simmons 0883^ Rainbolt + Coblentz
0886#\ this idea of possible positive e}ects of top pred!
ators should be kept in mind in conservation biology[
Acknowledgements
This work was supported by a Lavoisier fellowship
from the French Foreign O.ce\ by Biological Ocean!
ography Grant ONR] N99903!84!0!9923\ and endow!
ment funds from the John Dove Isaacs Chair in Natu!
ral Philosophy\ and was part of the IFRTP Program
No[ 168[ We thank Professor T[ Clutton!Brock\ Doc!
tors M[ de L[ Brooke\ S[ Lingle and P[ Rohani for
their helpful comments on the manuscript[
Þ 0888 British
Ecological Society
Journal of Animal
Ecology\ 57\ 171Ð181
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Received 07 February 0887^ revision received 05 June 0887
Appendix
SYSTEM "0Ð1#
There are several stationary states for the _rst system
"eqns 0\1#[ The _rst two equilibrium states ð9\ 9Ł and
ðKb\ 9Ł are always unstable[ The third state ð9\ S:hsŁ is
globally asymptotically stable if and only if rb ¾ hb:hs[
These three points always exist[ When no populations
go extinct\ the system reaches ðB\ S:hs ¦ B:hbŁ\
where B\ the bird population size at equilibrium\ is
the solution of a quadratic equation and therefore one
can have 9\ one or two equilibria with both popu!
lations present between 9 and Kb] B ð−t ¦
z"t1 − 3hsrbu#Ł:1hsrb\ with t hsKb − hsrb "Kb − S#\
and u "hb − hsrb#"SKb#[ Numerically\ when there are
two points with admissible coexistence\ one only\ at
most\ is stable[ If 9 ³ hb ¾ hs\ then there are two cases]
if hb:hs ¾ rb\ the point is stable\ otherwise it does not
exist[ If 9 ³ hs ¾ hb\ then there are two cases] if
hb:hs ³ rb\ it is stable\ if rb ¾ 0 ³ hb:hs it does not exist[
If 0 ³ rb ³ hb:hs\ then if hb × hb\ it does not exist\ if
hb hb\ it is stable\ if hb ³ hb there are two values
for this point[ hb "hsBmax1 ¦ rbhbSKb#:KbS\ with
Bmax ð"rb − 0#Kb − rbSŁ:1rb × 9[
SYSTEM "2Ð3#
The second system "eqns 2\ 3# has 2 stationary states[
P023] ð9\ 9Ł\ P123] ðKp\ 9Ł\ and P223] ðKp"0 − 0:rp#\
"0:mp#Kp"0 − 0:rp#Ł[ The dynamic behaviour of this
system is given by four cases[
181
Mesopredator
release in insular
ecosystems
0 Case 0] rc × 0] if rp ¾ 0 the system reaches P023\
otherwise it reaches P223[
1 Case 1] 9 ³ rp ¾ rc ³ 0] the system reaches P023[
2 Case 2] 9 ³ rc ³ 0\ rc ¾ rp] in this case\ the dynamics
depend on the initial proportion of prey and predator[
If C"9#:P"9# × mp"rp − rc#:"0 − rc#\ then the system
reaches P023[ If 9 ³ rc ¾ rp ³ 0\ then the system
reaches P023[ If 0 ³ rp\ then] "i# if rc ¦ rp × 1\ then
the system reaches P223^ "ii# if rc ¦ rp 1\ then this
stationary state becomes a centre\ all nearby trajectory
being periodical^ "iii# if rc ¦ rp ³ 1\ then this point is
unstable[
3 Case 3] rc 0] if 9 ³ rp ¾ 0\ the system reaches P023\
otherwise it reaches P223[
SYSTEM "4Ð6#
There are several equilibrium points for this system[
The two equilibrium points ðKb\ 9\ 9Ł and ð9\ S:hs\ 9Ł
always exist but are never stable[ There are 9\ one or
two equilibrium points where only the cat population
disappears\ since it is the solution of an equation of
the second degree ðB\ S:hs ¦ B:hb\ 9Ł[ These points
are never stable when they exist[ The point where only
the prey disappears ð9\ S"0 − 0:rr#:hs\ "0:mr# "S:hs#
"0 − 0:rr#Ł is admissible if rr × 0 and is stable if
rb ³ ðmb:mr ¦ hb"0 − 0:rr#:hsŁ and rc ¦ rr × 1[ The
point where only the mesopredator disappears
ðKb"0 − 0:rb#\ 9\ "0:mb#Kb"0 − 0:rb#Ł is admissible if
rb × 0 and is stable if rr ³ mr:mb and rc ¦ rb × 1[ In
numerical simulations\ at least one equilibrium point
with persistence of the three species ðB5\ R5\ C5Ł is
found if the above conditions are not ful_lled[
Þ 0888 British
Ecological Society
Journal of Animal
Ecology\ 57\ 171Ð181
SYSTEM "7Ð09#
Several equilibirum points arise[ Only the prey sur!
vive] ðKb\ 9\ 9Ł[ This point is stable if lr × rr and lc × rc[
Only the mesopredator survives] ð9\ "0 − lr:rr#S:hs\ 9Ł[
This point is stable if lr ³ rr\ lc × rc and lr ³ rr"0 −
rbhs:hb#[ Only the mesopredator disappears] ðKb"0 −
0:rb ¦ lc:rbrc#\ 9\ Kb"0 − 0:rb ¦ lc:rbrc#"0−lc:rc#:mbŁ[
This point is admissible if] rc × lc × rc"0 − rb#[ It is
stable if rc × lc × rc"0 − rb#\ lr × rr − mr:mb"0 − lc:rc#
and lc × "1 − rc − rb#:"1 − rc#[ The last condition
implies rc ³ 1\ which is ful_lled by studied cat popu!
lations in natura "e[g[ rc 9=32Ð9=44] Derenne 0865^
or 9=122Ð0=060] van Aarde 0867\ 0872#[ If not\ one
would have to replace it by] "1 − rc#lc × "1 − rc − rb#[
Only the prey disappears] ð9\ "0 − 0:rr ¦ lc:rrrc − lr:
rc#S:hs\
"0 − 0:rr ¦ lc:rrrc − lr:rc#"0 − lc:rc#S:mrhsŁ[
This point is admissible if] rc × lc × rc"0 − lrrr:
rc − rr#[ It is stable if rc × lc × rc"0 − lrrr:rc − rr#\
rb ³ mb"0 − lc:rc#:mc ¦ hb"0 − 0:rr ¦ lc:rrrc − lr:rc#:hs
and lc × rc"lr¦1 − rc − rr#:"1 − rc#[ The same com!
ment holds for the last condition "rc × 1#[ Only the
superpredator disappears] as in the case without
control\ there are 9\ 0 or 1 points\ given by the solu!
tions of an equation of the second degree[
ð−t 2 z"t1 − 3rrhshbu#:1rrhshb\ S:hs ¦ B:hb\ 9Ł\ with
here t lrhsKb ¦ rr ðhsKb − hsrb "Kb − S#Ł\ and
u lrhbSKb ¦ rr "hb − hsrb#"SKb#[ The point where
the superpredator disappears is unstable if lc ³ rc
"new introductions lead to other states#[ Numerically\
this point can be stabilized by increasing the value of
lc "increasing the control of the superpredator#[ In
numerical simulations\ at least one equilibrium point
with persistence of the three species ðB5\ R5\ C5Ł is
found if the above conditions are not ful_lled[